Tag: #GammaDistribution

Estimating Demand Without History

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My recent blogs discussed how to determine an Economic Lot Size to balance obsolescence, inventory, and changeover costs for perishable products when demand is uncertain.  I recommended using a Gamma distribution to model demand during the shippable life.  A Gamma distribution might also be used as basis for Statistical Safety stock calculations.  

Using a Gamma distribution to project demand variability requires a reliable basis for estimating the distribution. This would usually be based on several years of historical data. However, in times like this current pandemic, history is unreliable as a predictor of future demand. This blog will propose methods for estimating the Gamma distribution function when history is not valid.

I would like to borrow a concept from the Project Management Body of Knowledge (PMBOK), from the Project Management Institute. There are a few different ways it might be applied.

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Expected Obsolescence for a Given Starting Inventory

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For a product with a set shelf life, obsolescence will occur whenever units sold during the shippable life are less than the starting inventory at the beginning of that period. Varying demand can usually be modelled as a random variable following a probability distribution such as the gamma distribution (see my prior blog: A Probability Distribution for Demand Variability).       

The gamma probability density function is:

where is the gamma function. The mean of the gamma probability density function is ab and the standard deviation is .

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Production Quantity and Obsolescence with Demand Variability

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How much should I make when product has a fixed shelf life?  I should be OK if production does not exceed what I can sell on average before it goes out of code, right?  As Johnny Carson might have said, “You are wrong, bell curve breath!”

We live in a world that talks about averages all the time.  We assume if the expected average result meets our requirements, things will turn out fine. That is not necessarily true.  If it takes an average of 30 minutes to get to work, you should be fine leaving the house with 5 minutes to spare, right?  What if the average includes a one in five chance of being stopped by a train for ten minutes? Four out of five days you can get to work in 28 minutes and one out of five days it takes 38 minutes.   What time would you leave?

In real life, demand for your product fluctuates.  Because of the demand variability, there can be significant risk of obsolescence even when the production run is much less than average demand.   The best way to model this variability may be a gamma distribution (see my prior blog: A Probability Distribution for Demand Variability).  If so, the gamma probability density function can be used to estimate the expected number of units that will become obsolete for a given starting inventory. See how to calculate the expected obsolescence here.

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